Question 1081057
That form of equation is what could happen if you used the definition given directrix and focus, and derived the equation.  Yours is for parabola with horizontal symmetry axis, concave to the right.


Vertex is read from the equation:  (8,9).


Find y-intercepts:  Should be none.
{{{(y-9)^2=12(-8)}}}
{{{y-9=0+- sqrt(-96)}}}----you can see this will not be real numbers.


Find x-intercept:   {{{(0-9)^2=12(x-8)}}}
{{{12x-96=81}}}
{{{12x=81+96}}}
{{{12x=177}}}
{{{x=14.75}}}
Point   (14.75, 0).



{{{graph(400,400,-2,18,-2,18,9-sqrt(12x-96),9+sqrt(12x-96))}}}